The decimal and binary number systems are the world’s most commonly utilized number systems today.
The decimal system, also called the base-10 system, is the system we utilize in our daily lives. It utilizes ten figures (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent numbers. However, the binary system, also known as the base-2 system, uses only two digits (0 and 1) to depict numbers.
Understanding how to convert between the decimal and binary systems are essential for multiple reasons. For instance, computers utilize the binary system to portray data, so software engineers should be competent in changing within the two systems.
In addition, learning how to change among the two systems can helpful to solve math questions concerning large numbers.
This article will go through the formula for transforming decimal to binary, offer a conversion chart, and give examples of decimal to binary conversion.
Formula for Changing Decimal to Binary
The process of transforming a decimal number to a binary number is performed manually utilizing the following steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) collect in the previous step by 2, and record the quotient and the remainder.
Repeat the previous steps until the quotient is similar to 0.
The binary corresponding of the decimal number is acquired by reversing the series of the remainders obtained in the last steps.
This might sound complex, so here is an example to show you this method:
Let’s change the decimal number 75 to binary.
75 / 2 = 37 R 1
37 / 2 = 18 R 1
18 / 2 = 9 R 0
9 / 2 = 4 R 1
4 / 2 = 2 R 0
2 / 2 = 1 R 0
1 / 2 = 0 R 1
The binary equal of 75 is 1001011, which is obtained by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table showing the decimal and binary equals of common numbers:
Decimal | Binary |
0 | 0 |
1 | 1 |
2 | 10 |
3 | 11 |
4 | 100 |
5 | 101 |
6 | 110 |
7 | 111 |
8 | 1000 |
9 | 1001 |
10 | 1010 |
Examples of Decimal to Binary Conversion
Here are some instances of decimal to binary conversion employing the method discussed priorly:
Example 1: Convert the decimal number 25 to binary.
25 / 2 = 12 R 1
12 / 2 = 6 R 0
6 / 2 = 3 R 0
3 / 2 = 1 R 1
1 / 2 = 0 R 1
The binary equivalent of 25 is 11001, which is obtained by inverting the series of remainders (1, 1, 0, 0, 1).
Example 2: Convert the decimal number 128 to binary.
128 / 2 = 64 R 0
64 / 2 = 32 R 0
32 / 2 = 16 R 0
16 / 2 = 8 R 0
8 / 2 = 4 R 0
4 / 2 = 2 R 0
2 / 2 = 1 R 0
1 / 2 = 0 R 1
The binary equal of 128 is 10000000, that is achieved by reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
While the steps outlined earlier provide a way to manually convert decimal to binary, it can be time-consuming and error-prone for big numbers. Fortunately, other systems can be utilized to quickly and easily change decimals to binary.
For instance, you can employ the built-in functions in a spreadsheet or a calculator program to change decimals to binary. You can also utilize online tools such as binary converters, which allow you to type a decimal number, and the converter will automatically produce the corresponding binary number.
It is worth noting that the binary system has handful of constraints compared to the decimal system.
For instance, the binary system fails to illustrate fractions, so it is only suitable for representing whole numbers.
The binary system additionally needs more digits to portray a number than the decimal system. For example, the decimal number 100 can be represented by the binary number 1100100, that has six digits. The length string of 0s and 1s can be prone to typos and reading errors.
Last Thoughts on Decimal to Binary
In spite of these limitations, the binary system has several merits over the decimal system. For instance, the binary system is much simpler than the decimal system, as it just uses two digits. This simpleness makes it simpler to carry out mathematical operations in the binary system, for example addition, subtraction, multiplication, and division.
The binary system is more fitted to depict information in digital systems, such as computers, as it can easily be represented utilizing electrical signals. Consequently, understanding how to convert between the decimal and binary systems is important for computer programmers and for solving mathematical questions including large numbers.
Although the method of changing decimal to binary can be tedious and error-prone when worked on manually, there are applications which can rapidly convert within the two systems.
